A canon of mass 1100kg fires a cannonball of mass 6.2kg at a speed of 190ms-1.
a) Calculate the initial recoil speed of the cannon.
b)The purpose of the firing the canon is to transfer chemical energy of the explosive into kinetic energy of the cannon ball, but the cannon is also given kinetic energy. Calculate the percentage of the total kinetic energy that is carried by the cannon ball.
plz help I'm sure you'll agree that this question is confusing
thank you @Damon you make it seem not confusing! I wonder if you're a physics professor or something because u make it really easy
BSc in Physics, Ocean Engineering professor, retired.
You are welcome.
and error
percent = 100 (ball energy/total energy)
wow ocean engineer professor! thats really amazing, I hope one day ill become smart like you idol ! @Damon
Sure, I can help clarify the confusion and guide you through the solution step by step.
a) To calculate the initial recoil speed of the cannon, we can use the principle of conservation of momentum. According to this principle, the total momentum before firing the cannon is equal to the total momentum after firing.
The formula for momentum is:
Momentum = mass x velocity
Given:
Mass of the cannon = 1100 kg
Mass of the cannonball = 6.2 kg
Initial speed of the cannonball = 190 m/s
Let's assume the initial velocity of the recoil (cannon) is "v".
Before firing:
Total momentum = (Mass of the cannon + Mass of the cannonball) x 0 (since the cannon is at rest)
After firing:
Total momentum = Mass of the cannon x (-v) (since the cannon moves in the opposite direction with recoil speed "v") + Mass of the cannonball x velocity of the cannonball
Using the conservation of momentum equation:
(Mass of the cannon + Mass of the cannonball) x 0 = Mass of the cannon x (-v) + Mass of the cannonball x 190
Now we can solve for "v":
1100 kg x 0 = 1100 kg x (-v) + 6.2 kg x 190
Simplifying the equation:
0 = -1100v + 1178 kg m/s
Rearranging the equation to solve for "v":
1100v = 1178 kg m/s
v = 1178 kg m/s / 1100 kg
v ≈ 1.07 m/s
Therefore, the initial recoil speed of the cannon is approximately 1.07 m/s.
b) To calculate the percentage of the total kinetic energy carried by the cannonball, we need to compare the kinetic energy of the cannonball to the total kinetic energy of the system.
The formula for kinetic energy is:
Kinetic Energy = 0.5 x mass x (velocity)^2
Given:
Mass of the cannonball = 6.2 kg
Initial speed of the cannonball = 190 m/s
The initial kinetic energy of the cannonball is given by:
Kinetic Energy of the cannonball = 0.5 x 6.2 kg x (190 m/s)^2
Now, we need to calculate the total kinetic energy of the system. This includes both the kinetic energy of the cannonball and the kinetic energy of the cannon.
To find the kinetic energy of the cannon:
Kinetic Energy of the cannon = 0.5 x mass of the cannon x (recoil speed of the cannon)^2
Substituting the known values:
Kinetic Energy of the cannon = 0.5 x 1100 kg x (1.07 m/s)^2
Now, calculate the total kinetic energy:
Total Kinetic Energy = Kinetic Energy of the cannonball + Kinetic Energy of the cannon
Finally, calculate the percentage of the total kinetic energy carried by the cannonball:
Percentage = (Kinetic Energy of the cannonball / Total Kinetic Energy) x 100
By plugging in the calculated values, you can determine the percentage of the total kinetic energy carried by the cannonball.
1100 v + 6.2 * 190 = 0
energy of ball = (1/2)(6.2)(190)^2
energy of cannon = (1/2)(1100) v^2
total = sum of those
percent = 100 (ball energy/cannon energy)
No, I do not think it is confusing.